Matrix Cracking in Non-Symmetric Laminates under Combined Membrane and Flexural Loading

A constitutive model of progressive matrix cracking in fiber reinforced laminated composites is developed for the case of both membrane and flexural deformation. The analytical progressive damage model addresses both the degraded mechanical properties of the laminate for given levels of matrix cracking in individual plies, and the matrix cracking damage growth under applied loading. There is no limitation on the configuration of the laminate or on the number of the cracking plies, as it is the case of the most models available in the literature, where only symmetric laminate stacking sequences (LSS) are addressed, or only certain plies can undergo matrix cracking. The proposed analytical model takes into account the effect of crack closure under flexural deformation. The model also considers the experimentally observed fracture toughness strenghtening of the material with increasing damage level, usually referred to as 'Resistance-curve (R-curve)' behavior. Crack densities in individual plies of the laminates are the damage state variables of the model. This formulation is unlike the progressive damage models for laminated composites implemented in most of the FEA commercial packages, where softening laws are considered in order to describe stiffness reduction and damage evolution. By using the ply crack densities as state variables the model is able to predict and to keep track of the crack density in individual plies during the loading history, which can be of interest in application where the permeability (leakage) of the laminate is a limiting design factor. One example of this kind of application can be pressure vessels containing fluids or gases. Thermal residual stresses are taken into account in the present model, which extends the predictive capabilities of the model to applications in the range of cryogenic temperatures. The analytical model is validated against available experimental data for the case of both membrane and flexural loading.